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Robustness analysis of blind watermarking for quality scalable image compression


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Bhowmik, D. and Abhayaratne, C. (2010) Robustness analysis of blind watermarking for

quality scalable image compression. In: 18th European Signal Processing Conference

(EUSIPCO-2010), August 23-27 2010, Aalborg, Denmark.

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Deepayan Bhowmik, Charith Abhayaratne and Matthew Oakes

Department of Electronic and Electrical Engineering, The University of Sheffield Sheffield S1 3JD, United Kingdom.

{d.bhowmik, c.abhayaratne, m.oakes}@sheffield.ac.uk


Robustness analysis of a blind wavelet based ranked-ordered watermarking scheme against quality scalable image com-pression is presented in this paper. The analysis considers a general wavelet-based compression scheme by modeling the bit-plane discarding, used in achieving quality scalabil-ity in JPEG2000. In this work we aim to improve the ro-bustness by proposing the optimum modification for the se-lected coefficients in order to retain the watermark informa-tion. A relationship is established between the watermark detection algorithm and the number of bit planes discarded and this knowledge is used during the embedding procedure. The proposed model assumes the same embedding and com-pression wavelet kernel. The experimental results verify the proposed model and demonstrate improved performance in robustness to quality scalable compression in JPEG2000.


In recent years, there has been an increase in use of scalable coded media. JPEG2000 (Joint Photographic Experts Group) for image coding and H.264/MPEG-4 advanced video cod-ing (AVC) scalable extension are the main standards used in universal multimedia access (UMA) applications for seam-less media content delivery. Digital watermarking addresses the issues related to multimedia security and digital rights management. In this context an increasing number of wavelet domain watermarking schemes are offered consid-ering JPEG2000 image compression [1–5].

In UMA multimedia usage scenario, the emerging wa-termarking algorithms attempt to improve the robustness against scalable coding, either by incorporating the water-marking into the compression algorithm, as in JPEG 2000 Secured (JPSec) [6], or employing other wavelet domain em-bedding schemes independent of compression scheme. For example, in [7], a secure signature scheme is presented based on JPEG2000 image authentication. However, most of the algorithms do not provide an insight into how robust these algorithms to quality scalability or resolution scalability in JPEG2000 scalable image compression. Common models restrict their focus only on robustness to image processing and geometric attacks or conventional compression [8].

In this paper we present a model for improving the wavelet based blind watermarking robustness to quality scal-able image compression attacks. To emulate the compres-sion in JPEG2000, the wavelet based comprescompres-sion using a bit plane discarding model is considered. The model is derived

The work of Mr Bhowmik is supported by the BP-EPSRC Dorothy Hodgkin Postgraduate Award and the work of Mr Oakes is supported by the EPSRC Doctoral Training Award.

by analyzing the effect of compression parameters in scalable image coding. In our previous work [9], the robustness of a non-blind watermarking scheme is analysed whereas here we have consider blind watermarking scheme and exploited a ranked-order-based blind watermarking algorithm described in [4]. The model shows the relationship between the com-pression parameters and the wavelet coefficients to be modi-fied and uses that relationship to identify the optimum mod-ification during watermark embedding. The proposed water-mark embedding criteria ensures improved robustness under various quality scalability adaptations of JPEG2000 encoded bitstream. At the same time to improve the imperceptibility, an imperceptibility model [10] may be used to find the trade off. Without loosing the generality, we have implemented the model with an example case in [4]. However other blind watermarking algorithms can be modeled with a similar ap-proach.

The rest of the paper is organized with a brief descrip-tion on the general scalable coding framework and wavelet-based quantization error modeling in Sec. 2. A discussion is presented in Sec. 3 on the generalised framework of wavelet based watermarking schemes. The robustness model is pre-sented in Sec. 4 followed by the experimental results in Sec. 5 with concluding remarks in Sec. 6.


UMA uses scalable coded content to enable seamless mul-timedia consumption independent of the application device, network media, network speed, resource limitation and usage preferences. The input media is coded in such a way that the main host server keeps the full resolution content which can be decoded to produce maximum quality and spatial resolu-tion. The supply of the scaled content, to a less capable dis-play or to transmit through the lower bandwidth, is adapted in different nodes having different scaling parameters. At each node the scaling parameters might be different and a new bit stream can be generated. Finally a suitable decoded version is supplied to the end-user display terminals.

JPEG2000 uses the Discrete Wavelet Transform (DWT) as its core technology and offers scalable decoding with qual-ity and resolution scalabilqual-ity. The scalable coders encode the image by performing the DWT followed by embedded quan-tizing and entropy coding. The coefficient quantization, in its simplest form, can be formulated as follows:



, (1)


Figure 1: Quantization compression scheme considering N level bit-plane discarding.

often useQ=2N, whereNis a non-negative integer. Such a quantization parameter within downward rounding (i.e., us-ingfloor), can also be interpreted as bit plane discarding as commonly known within the image coding community.

At the decoder side, a reverse process of the encoding is followed to reconstruct the image. The dequantization pro-cess is formulated as follows:




1 2


, (2)

where ˆCis the dequantized coefficient. In such a quantization scheme, the original coefficient values in the range k.Q≤

C<(k+1).Q, wherek∈ ±1,±2±3...andQ=2N for bit plane wise coding are mapped to ˆC=Ck, which is the center value of the concerned region as shown in Fig. 1.


In an attempt to generalization of wavelet based watermark-ing schemes, we have accommodated popular algorithms into a common framework [11] by dissecting the algorithms into common functional modules and deriving a basic em-bedding form as follows:

Cm,n=Cm,n+∆m,n, (3)

whereCm,nis the modified coefficient at(m,n)position,Cm,n is the coefficient to be modified and ∆m,n is the modifica-tion due to watermark embedding. Based on the modificamodifica-tion algorithms we have broadly categorized the algorithms into two groups: direct modification [1, 2] and quantization based modification [3–5]. The watermarking algorithms can also be grouped in two different categories: (1) Non-blind wa-termarking where the original image is required during the watermark extraction procedure and (2) Blind watermarking (no original host image needed). Due to the nature of em-bedding most of the direct modification algorithms defined under non-blind category where as majority of the quantiza-tion based schemes can be referred as blind.

Direct modificationDirect modification algorithms are generalized in the following modification value∆m,nat(m,n) position:

∆m,n= (a1)α(Cm,n)bWm,n+ (a2)vm,nWm,n

+(a3)βCw+ (a4)Sm,n, (4)

wherea1, ...,a4are Boolean variables to identify the presence

of each of the components for a given methodology,Cm,nis the coefficient to be modified,αis the watermark weighting factor,b=1,2...is the watermark strength parameter,Wm,nis

the watermark value,vm,nis the weighting parameter based on pixel masking in a human visual system model, β is an HVS-based fusion strength parameter in the case of fusion based scheme,Cw is the watermark wavelet coefficient and

Sm,nis any other value which is normally a function ofCm,n.

Quantization based modificationThe ranked ordered list based algorithms change the median value of a local area (typically a 3x1 coefficient window) considering the neigh-boring values. The modification value∆m,nis decided based on a quantization stepδ(−δ≤∆m,n≤δ) within the range of the selected 3x1 window. Different functions are suggested in the literatures to find the value of δ and the functions normally consists of minimum (Cmin) and maximum (Cmax) value of the coefficients in each selected window.

δ=f(α,Cmin,Cmax), (5)

whereαis the weighting factor and predefined. These meth-ods vary by the way the coefficients are chosen for the list, for example, choosing from the same subband (intra subband quantization) [4] and choosing from different subbands of the same level (inter subband quantization) [3].


A ranked order based blind watermarking scheme [4] has been adopted here as the example case. As described pre-viously in Sec. 3, a non-overlapping 3×1 running window is passed through the entire selected subband of the wavelet decomposed image. At each sliding position, a rank order sorting is performed on the coefficientsC1,C2andC3to

ob-tain an ordered listC1<C2<C3. The median valueC2 is

modified to obtainC2′ as follows:

C′2= f(α,C1,C3,w), (6)

wherewis the input watermark sequence and f()denotes a non-linear transformation. Referring Eq. (5), the quantiza-tion stepδ is defined here as:


2 , (7)

whereα is the watermark strength parameter.

For the extraction of watermark bit sequence, the DWT is performed on the test image followed by a rank ordered sort-ing with a 3×1 running window to obtain sorted elements

C1,C2andC3at each position. The watermarked bitwext as-sociated with the particular window position is extracted as follows:

wext∈(0,1) =







%2, (8)

where % denotes the modulo operator to detect odd or even number.

At this point we considered the quality scalable com-pression on test image and find the parameter which affects the robustness. We have defined a superscriptq to each of the previously defined notations to represent the quantization compression includingC1,C2,C3andδtoC1q,C







Figure 2: Mapping of coefficients after quantization com-pression consideringNbit planes discarding.

the watermark extraction will be based on these new values. At this point, with the example of any selected window, we assume,C1is mapped toCk(=C1q),C2is mapped toCk+m (=C2q) andC3is mapped toCk+n(=C3q) as shown in Fig. 2,

wherek,m,n∈ ±1,±2±3...To extract the watermark, new quantized values are taken in consideration. With reference to Eq. (2) and Eq. (7), the watermark quantization step value δqcan be now defined as:

δq= α|Cq1|+|C



2 , = αCk+Ck+n

2 . (9)

Using Eq. (2), we can write the center values of a cluster in Eq. (9) consideringNbit planes are discarded:

δq= αk.2N+2N−1

2 +(k+n).2N+2



2 ,

= α.2N−1.(2k+n+1)0.5α,

≈ α.2N−1.(2k+n+1), (10)

where considering a typical α =0.1 or 0.05 and the 0.5α term is ignored as this term is much smaller than the first part of the equation. With reference to Eq. (8) and Eq. (10), the extracted watermark bitwext can be expressed with the following equation:

wext∈(0,1) =








= [Ck+m−Ck




= [

(k+m).2N+2N−1 2 −k.2N−2






= [1



%2, (11)

where % denotes the modulo operator to identify odd or even number with the condition that 0<m≤n.

Thus using Eq. (11), it is possible to predictwext at a given number of discarded bit planes. We can use this re-lationship during the watermark embedding procedure. For any selected 3x1 running window,C1 andC3are not being

modified and hence it is possible to know the values ofkand

nin Eq. (11), whereα is an user defined known parameter. Therefore the value ofmcan be decided during embedding in order to extract ′1′ or ′0′ correctly atN number of dis-carded bit planes. Based on the input watermark sequence andC2 value, the optimumC2′ value can be calculated, so

that wext sequence will be the same as the input watermark sequence. One can calculate the similar optimum value ofC2

for any otherNvalue and find the common suitable optimum

C2′ value for anyNor lower number of bit plane discarding.

Table 1: Values ofmand correspondingwext andC2q

m wext C2q

1 1 79.5

2 1 111.5

3 0 143.5

4 0 175.5


5 1 207.5

Table 2: Ranges ofC2′ to embed′1′and′0′ for differentN

being discarded

N→ 3 4 5 Combined

Embed 184-192 & 160-176 & 192-224 192-200

1192-200 192-208

Embed 176-184 & 128-144 & 160-192 176-184

0200-208 176-192

For an example, we assumeC1=35,C2=181,C3=203

andα=0.1. Referring to Eq. (11) atN=5, other variables can be calculated ask=1,n=5 andwext= [2.5m]%2. Now for different values of mwe can estimate the value ofwext andC2qas shown in Table 1.

Embed′1′:Based on the originalC2value and with

ref-erence to calculated m, atN=5, with minimum modifica-tion, the modified median coefficient C2′ should be in the range of 192≤C2′<224 to embed′1′for a correct extraction.

Embed′0′:Similarly using Table 1 the range for embed-ding′0′can be calculated as 160≤C′2<192.

The similar calculation can be done forN=1,2,3,4... and the range forC′2can be found for a given 3x1 running window. The overlapping range for allN value can ensure correct watermark extraction at a givenN or lower number of bit planes discarding. As an example case, we extended our previous example forN=3,4..and calculated the range to embed′1′ or′0′ as shown in Table 2. Now based on the calculated values for the modifiedC2′, to embed′1′the coef-ficient must be within (192−200) and to embed′0′the range will be (176−184) in order to retain the watermark informa-tion atN=3,N=4 orN=5.

Hence using the above relationship we can optimally em-bed the watermark sequence in the example watermarking scheme for a guaranteed watermark extraction at a given compression ratio. Using a similar model, the watermark em-bedding criteria for any other blind watermarking schemes such as in [3, 5] can be derived for better robustness perfor-mance.



arrange-ments are shown below:

Experiment Set 1: Here we have considered the bit plane based quality compression effect. Firstly the embed-ding is done as it is suggested in [4], without considering the derived model. Then using the model, the wavelet coeffi-cients are modified assuming different number of discarded bit planes (N) at the time of watermark embedding. The qual-ity scalabilqual-ity is applied on watermarked image by discard-ing different number of bit-planes corresponddiscard-ing to quanti-zation step Q=2N. The watermark is extracted from the compressed image and the Hamming distance is measured between the extracted and the original watermark. The re-sults are shown in Fig. 3 with x axis representing quantization stepQand Hamming distance in y axis. A bi-orthogonal 9/7 wavelet kernel is considered here for embedding and com-pression in 3 level wavelet decomposition with α value of 0.08. In all cases the low frequency subband is considered for the watermark embedding.

Experiment Set 2: A similar experimental set up as in Experiment Set 1, is followed except the compression sce-nario. A JPEG2000 compression is applied to the water-marked images and the test images are produced at various compression ratio. The results are shown in Fig. 4 where x axis represents the compression ratio and y axis shows the hamming distance.

In both the experimental set up first two graphs repre-sent individual image performances whereas the third graphs show the average Hamming distance for 31 test images within 95% confidence interval.


The robustness model derived here establishes the rela-tionship between the quantization compression parameters and the choice of wavelet coefficients of the host image to be modified. The experimental simulations were performed by the optimum modification of the selected coefficients us-ing the derived model. Firstly, the watermark embeddus-ing is performed with the original algorithm and robustness is mea-sured against different compression scenario, i.e., different number of bit plane discarding. Then we embedded the wa-termark assuming different bit plane discarding (N=1 : 5) and modified the wavelet coefficients accordingly. The ex-perimental results shown in Fig. 3 indicates that the robust-ness is improved as more number of bit planes are consid-ered during embedding. Hence the watermark is more ro-bust to compression if higher value ofNis considered during watermark embedding. This model also strongly supports JPEG2000 based quality scalable compression as shown in Fig. 4. Higher the N value considered during embedding gives better robustness. But at very high compression ratio the test images do not retain watermark information as the image pixel information is lost significantly. As a result a higher Hamming distance is noticed as shown in the figures. As we conclude that a higher N value during embed-ding offers better robustness but at the same time it may cause higher embedding distortion. One can optimize the watermarking scheme to offer lower distortion and higher ro-bustness by combining this model with the imperceptibility model in our previous work [10].


A mathematical analysis of robustness was presented in this work with reference to a blind wavelet-based watermarking scheme with reference to quantization based quality scalable

0 1 2 3 4 5 6 7

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Robustness against bit plane discarding−based compression

Quantisation Step: 0=1, 1=2, 3=4, 3=8, 4=16, 5=32, 6=64, 7=128

Hamming Distance

Algorthm in [4] N=1 N=3 N=5 N=6

0 1 2 3 4 5 6 7

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Robustness against bit plane discarding−based compression

Quantisation Step: 0=1, 1=2, 3=4, 3=8, 4=16, 5=32, 6=64, 7=128

Hamming Distance

Algorthm in [4] N=1 N=3 N=5 N=6

Figure 3: Robustness performance against quantization based compression for image 1 (Row 1), image 2 (Row 2) and average performance of 31 images (Row 3). Quantiza-tion steps:Q=21,Q=22...Q=26.N= number of bit plane considered during embedding.


0 2 4 6 8 10 12 14 0.05

0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55

Robustness against JPEG2000 compression

bpp: 0=8, 1=4, 3=2, 3=1, 4=0.9, 5=0.8, 6=0.7, 7=0.6, 8=0.5, 9=0.4, 10=0.3, 11=0.2, 12=0.1

Hamming Distance

Algorthm in [4] N=1 N=3 N=5

0 2 4 6 8 10 12 14

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Robustness against JPEG2000 compression

bpp: 0=8, 1=4, 3=2, 3=1, 4=0.9, 5=0.8, 6=0.7, 7=0.6, 8=0.5, 9=0.4, 10=0.3, 11=0.2, 12=0.1

Hamming Distance


Algorthm in [4] N=1 N=3 N=5

Figure 4: Robustness performance against JPEG2000 com-pression for image 1 (Row 1), image 2 (Row 2) and average performance of 31 images (Row 3).N= number of bit plane considered during embedding.

such as quantization step. Then necessary conditions were made to optimally modify the coefficients which can retain the watermark information at a given compression ratio. A bit-plane discarding based compression is considered to

de-rive the scheme and experimental verification is done for the same. The derived model is also supported by experimental simulations against JPEG2000 compressions. Such an analy-sis is very useful to optimize the modification of the selected coefficient during watermark embedding which helps to re-duce the embedding distortion while keeping better robust-ness.


[1] X. Xia, C. G. Boncelet, and G. R. Arce, “Wavelet trans-form based watermark for digital images,” Optic Ex-press, vol. 3, no. 12, pp. 497–511, Dec. 1998.

[2] J. R. Kim and Y. S. Moon, “A robust wavelet-based dig-ital watermarking using level-adaptive thresholding,” in

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[3] D. Kundur and D. Hatzinakos, “Digital watermarking using multiresolution wavelet decomposition,” inProc. IEEE ICASSP, 1998, vol. 5, pp. 2969–2972.

[4] L. Xie and G. R. Arce, “Joint wavelet compression and authentication watermarking,” inProc. IEEE ICIP, 1998, vol. 2, pp. 427–431.

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[6] T. Ebrahimi and R. Grosbois, “Secure JPEG 2000-JPSEC,” 2003, vol. 4, pp. 716–719.

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[8] M. Ejima and A. Miyazaki, “On the evaluation of per-formance of digital watermarking in the frequency do-main,” inProc. IEEE ICIP, 2001, vol. 2, pp. 546–549. [9] D. Bhowmik and C. Abhayaratne, “The effect of

qual-ity scalable image compression on robust watermark-ing,” inProc. IEEE DSP’09, 2009, pp. 1–8.

[10] D. Bhowmik and C. Abhayaratne, “A generalised model for distortion performance analysis of wavelet based watermarking,” inProc. IWDW ’08, Lect. Notes in Comp. Sc., 2008, vol. 5450, pp. 363–378.


Figure 1: Quantization compression scheme considering Nlevel bit-plane discarding.
Table 1: Values of m and corresponding wext and Cq2
Fig. 4. Higher the N value considered during embedding
Figure 4: Robustness performance against JPEG2000 com-pression for image 1 (Row 1), image 2 (Row 2) and averageperformance of 31 images (Row 3)


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